Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26012398 | C2 | direct (N × H) |
| 7. C22×Dic346 | C4 | semidirect |
| 10. #19149667 | C4 | semidirect |
| 13. C2×C42×C173 | C4 | semidirect |
| 21. C2×Dic346 | C2×C4 | semidirect |
| 33. C42×C173 | C2×C4 | semidirect |
| 73. C2×C173 | #354 | semidirect |
| 77. C173 | C2×#354 | semidirect |
| 89. C2×C42 | #10621924 | semidirect |
| 111. C42 | C2×#10621924 | semidirect |
| 153. C2 | #26012398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149738 | 2 |
| #26012398 | 2 |
| C2×#19149667 | 2 |
| C2×#354 | 173 |